How do you divide $\frac{- x^{4} + 6 x^{3} + 8 x + 12}{x^{2} - 3 x + 9}$ $(-x^4+6x^3+8x+12)/(x^2-3x+9)$ ?

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How do you divide $\frac{- x^{4} + 6 x^{3} + 8 x + 12}{x^{2} - 3 x + 9}$ $(-x^4+6x^3+8x+12)/(x^2-3x+9)$ ?

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Answer 1 · 2016-05-17T12:59:55

Dividing $- x^{4} + 6 x^{3} + 8 x + 12$ $-x^4+6x^3+8x+12$ by $x^{2} - 3 x + 9$ $x^2-3x+9$ ,

the quotient is $- x^{2} + 3 x + 18$ $-x^2+3x+18$ and remainder is $35 x - 150$ $35x-150$

Explanation:

To divide $- x^{4} + 6 x^{3} + 8 x + 12$ $-x^4+6x^3+8x+12$ by $x^{2} - 3 x + 9$ $x^2-3x+9$ ,

as $- \frac{x^{4}}{x^{2}} = - x^{2}$ $-x^4/x^2=-x^2$ .

Now $- x^{2} \times (x^{2} - 3 x + 9) = - x^{4} + 3 x^{3} - 9 x^{2}$ $-x^2xx(x^2-3x+9)=-x^4+3x^3-9x^2$

Subtracting $- x^{4} + 3 x^{3} - 9 x^{2}$ $-x^4+3x^3-9x^2$ from $- x^{4} + 6 x^{3} + 8 x + 12$ $-x^4+6x^3+8x+12$ , we get

$(- x^{4} + 6 x^{3} + 8 x + 12) - (- x^{4} + 3 x^{3} - 9 x^{2}) = 3 x^{3} + 9 x^{2} + 8 x + 12$ $(-x^4+6x^3+8x+12)-(-x^4+3x^3-9x^2)=3x^3+9x^2+8x+12$

Now in similar way $3 x^{3} + 9 x^{2} + 8 x + 12$ $3x^3+9x^2+8x+12$ , $x^{2} - 3 x + 9$ $x^2-3x+9$ can go $3 x$ $3x$ times and remainder will be

$3 x^{3} + 9 x^{2} + 8 x + 12 - 3 x (x^{2} - 3 x + 9)$ $3x^3+9x^2+8x+12-3x(x^2-3x+9)$

= $3 x^{3} + 9 x^{2} + 8 x + 12 - 3 x^{3} + 9 x^{2} - 27 x$ $3x^3+9x^2+8x+12-3x^3+9x^2-27x$

= $18 x^{2} - 19 x + 12$ $18x^2-19x+12$

Now in this, $x^{2} - 3 x + 9$ $x^2-3x+9$ goes $18$ $18$ times and remainder is

$18 x^{2} - 19 x + 12 - 18 (x^{2} - 3 x + 9) = - 19 x + 54 x + 12 - 162 = 35 x - 150$ $18x^2-19x+12-18(x^2-3x+9)=-19x+54x+12-162=35x-150$

Hence when we divide $- x^{4} + 6 x^{3} + 8 x + 12$ $-x^4+6x^3+8x+12$ by $x^{2} - 3 x + 9$ $x^2-3x+9$ , the quotient is $- x^{2} + 3 x + 18$ $-x^2+3x+18$ and remainder is $35 x - 150$ $35x-150$

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How do you divide $\frac{- x^{4} + 6 x^{3} + 8 x + 12}{x^{2} - 3 x + 9}$ $(-x^4+6x^3+8x+12)/(x^2-3x+9)$ ?

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How do you divide (-x^4+6x^3+8x+12)/(x^2-3x+9)−x4+6x3+8x+12x2−3x+9(-x^4+6x^3+8x+12)/(x^2-3x+9)?

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How do you divide $\frac{- x^{4} + 6 x^{3} + 8 x + 12}{x^{2} - 3 x + 9}$ $(-x^4+6x^3+8x+12)/(x^2-3x+9)$ ?